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Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras (2301.12385v2)
Published 29 Jan 2023 in math.RT
Abstract: In this paper, we present a method of symplectic double extensions for restricted quasi-Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent obstructions to symplectic double extension, which we fully describe. We found a necessary condition for which a restricted quasi-Frobenius Lie superalgebras is a symplectic double extension of a smaller restricted Lie superalgebra. The constructions are illustrated with a few examples.